Equations of motion: I don't understant why "i" doesn't show up

[ggu]

Equations of motion: I don't understant why "i" does't show up

When solving: m y''+2r y'+k y = 0, we get a result of Ce^(-3t+it) + De^(-3t-it)
and as per e^it = cos t +i sin t they say the result is (C+D ) e^(-3t) cos t + (C-D) e^(-3t) sin t
i don't understant why i doesn't show up, i'm wondering if they made a mistake and should be
(C+D ) e^(-3t) cos t + (C-D) e^(-3t) i sin t

Any help please!

 

[Deleted member 4993]

When solving: m y''+2r y'+k y = 0, we get a result of Ce^(-3t+it) + De^(-3t-it)
and as per e^it = cos t +i sin t they say the result is (C+D ) e^(-3t) cos t + (C-D) e^(-3t) sin t
i don't understant why i doesn't show up, i'm wondering if they made a mistake and should be
(C+D ) e^(-3t) cos t + (C-D) e^(-3t) i sin t

Any help please!

Did you expand and try to simplify: Ce^(-3t+it) + De^(-3t-it) ?

 

[ggu]

Did you expand and try to simplify: Ce^(-3t+it) + De^(-3t-it) ?

yes, exactly and i can't get rid of i sin t contrary of the solution being sin t

you can see the solution here at 23:40 http://ocw.mit.edu/resources/res-18...derivatives/differential-equations-of-motion/